Questions: The car lift in a gas station operates with an air pressure of 2,000 kPa. The piston of the car lift has a diameter of 30.0 cm. What is the m

Solution Steps

We need to find the maximum force that the car lift can exert using the given air pressure and the diameter of the piston's circular cross-section.

The diameter of the piston is given as 30.0 cm. We need to convert this to meters for consistency with the pressure unit (kPa): \[ \text{Diameter} = 30.0 \, \text{cm} = 0.300 \, \text{m} \]

The radius \( r \) of the piston is half of the diameter: \[ r = \frac{0.300 \, \text{m}}{2} = 0.150 \, \text{m} \]

The area \( A \) of the circular piston is given by the formula for the area of a circle: \[ A = \pi r^2 = \pi (0.150 \, \text{m})^2 \] \[ A = \pi \times 0.0225 \, \text{m}^2 \] \[ A \approx 0.0707 \, \text{m}^2 \]

The force \( F \) exerted by the piston is the product of the pressure \( P \) and the area \( A \): \[ F = P \times A \] Given \( P = 2000 \, \text{kPa} = 2000 \times 10^3 \, \text{Pa} \), we have: \[ F = 2000 \times 10^3 \, \text{Pa} \times 0.0707 \, \text{m}^2 \] \[ F = 141,400 \, \text{N} \]

Final Answer